Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
394 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C7×#107 | C2 | semidirect |
| 3. #11727498 | C2 | semidirect |
| 4. #11725291 | C2 | semidirect |
| 11. #89467 | C4 | semidirect |
| 14. C4×D56 | C4 | semidirect |
| 15. #89454 | C4 | semidirect |
| 49. C4×#107 | D7 | semidirect |
| 237. C7 | #11742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735915 | 2 |
| C4×C7×#107 | 2 |
| #11727498 | 2 |
| #11725291 | 2 |
| #11742 | 7 |